In the figure, instantaneous rate of change of f(x) at all the points between x = a and x =b is given by the slope of the secant AB.

True

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False

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Solution

The correct option is B
False

Instantaneous rate of change of f(x) at a point on the graph is equal to the slope of the tangent at that point, whenever a tangent can be drawn at that point. There could be(in fact there will be at least one) some points between x = a and x = b where the slope of the tangent is equal to the slope of the secant AB. This does not mean that this is true for all the points between a and b. So, the given statement is false.

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